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We present a solution of the full TDDFT eigenvalue equation in the linearresponse formalism exhibiting a linear-scaling computational complexity withsystem size, without relying on the simplifying Tamm-Dancoff approximation(TDA). The implementation relies on representing the occupied and unoccupiedsubspace with two different sets of in situ optimised localised functions,yielding a very compact and efficient representation of the transition densitymatrix of the excitation with the accuracy associated with a systematic basisset. The TDDFT eigenvalue equation is solved using a preconditionedconjugate-gradients algorithm that is very memory-efficient. The algorithm isvalidated on a test molecule and a good agreement with results obtained fromstandard quantum chemistry packages is found, with the preconditioner yieldinga significant improvement in convergence rates. The method developed in thiswork is then used to reproduce experimental results of the absorption spectrumof bacteriochlorophyll (BChl) in an organic solvent, where it is demonstratedthat the TDA fails to reproduce the main features of the low energy spectrum,while the full TDDFT equation yields results in good qualitative agreement withexperimental data. Furthermore, the need for explicitly including parts of thesolvent into the TDDFT calculations is highlighted, making the treatment oflarge system sizes necessary that are well within reach of the capabilities ofthe algorithm introduced here. Finally, the linear-scaling properties of thealgorithm are demonstrated by computing the lowest excitation energy of BChl insolution. The largest systems considered in this work are of the same order ofmagnitude as a variety of pigment-protein complexes, opening up the possibilityof studying their properties without having to resort to any semiclassicalapproximations to parts of the protein environment.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

Linear-scaling time-dependent density-functional theory (TDDFT) beyond  the Tamm-Dancoff approximation: obtaining efficiency and accuracy with in  situ optimised local orbitals